a r X i v :h e p -e x /0110016v 1 9 O c t 2001RUTGERS-01-88Radiative Decay Width Measurements ofNeutral Kaon Excitations Using thePrimakoffEffectA.Alavi-Harati 12,T.Alexopoulos 12,M.Arenton 11,K.Arisaka 2,S.Averitte 10,R.F.Barbosa 7,∗∗,A.R.Barker 5,M.Barrio 4,L.Bellantoni 7,A.Bellavance 9,J.Belz 10,D.R.Bergman 10,E.Blucher 4,G.J.Bock 7,C.Bown 4,S.Bright 4,E.Cheu 1,S.Childress 7,R.Coleman 7,M.D.Corcoran 9,G.Corti 11,B.Cox 11,A.Cunha 10,A.R.Erwin 12,R.Ford 7,A.Glazov 4,A.Golossanov 11,G.Graham 4,J.Graham 4,E.Halkiadakis 10,J.Hamm 1,K.Hanagaki 8,S.Hidaka 8,Y.B.Hsiung 7,V.Jejer 11,D.A.Jensen 7,R.Kessler 4,H.G.E.Kobrak 3,Due 5,th 10,A.Ledovskoy 11,P.L.McBride 7,D.Medvigy 10,P.Mikelsons 5,E.Monnier 4,∗,T.Nakaya 7,K.S.Nelson 11,H.Nguyen 7,V.O’Dell 7,R.Pordes 7,V.Prasad 4,X.R.Qi 7,B.Quinn 4,E.J.Ramberg 7,R.E.Ray 7,A.Roodman 4,S.Schnetzer 10,K.Senyo 8,P.Shanahan 7,P.S.Shawhan 4,J.Shields 11,W.Slater 2,N.Solomey 4,S.V.Somalwar 10,†,R.L.Stone 10,E.C.Swallow 4,6,S.A.Taegar 1,R.J.Tesarek 10,G.B.Thomson 10,P.A.Toale 5,A.Tripathi 2,R.Tschirhart 7,S.E.Turner 2,Y.W.Wah 4,J.Wang 1,H.B.White 7,J.Whitmore 7,B.Winstein 4,R.Winston 4,T.Yamanaka 8,E.D.Zimmerman 41University of Arizona,Tucson,Arizona 857212University of California at Los Angeles,Los Angeles,California 900953University of California at San Diego,La Jolla,California 920934The Enrico Fermi Institute,The University of Chicago,Chicago,Illinois 606375University of Colorado,Boulder,Colorado 803096Elmhurst College,Elmhurst,Illinois 601267Fermi National Accelerator Laboratory,Batavia,Illinois 605108Osaka University,Toyonaka,Osaka 560-0043Japan9Rice University,Houston,Texas 7700510Rutgers University,Piscataway,New Jersey 0885411The Department of Physics and Institute of Nuclear and Particle Physics,University of Virginia,Charlottesville,Virginia 2290112University of Wisconsin,Madison,Wisconsin 53706∗Permanent address C.P.P.Marseille/C.N.R.S.,France∗∗Permanent address University of S˜a o Paulo,S˜a o Paulo,Brazil†To whom correspondence should be addressed.Electronic address:somalwar@The KTeV CollaborationAbstractWe produce a sample consisting of147candidate events,with minimal backgrounds,of the mixed axial vector pair(K1(1270)-K1(1400))by excitingK L’s in the Coulombfield of lead and report thefirst measurements of theradiative widthsΓr(K1(1400))=280.8±23.2(stat)±40.4(syst)keV andΓr(K1(1270))=73.2±6.1(stat)±28.3(syst)keV.We also place90%CL upperlimitsΓr(K∗(1410))≤52.9keV for the vector state andΓr(K∗2(1430))≤5.4keV for the tensor state.These measurements allow for significant tests ofquark-model predictions of radiative widths for the low-lying vector mesons.Several resonant excitations of the neutral kaon are known to exist[1],most having been observed indirectly using partial wave analysis[2].Figure1is a schematic repre-sentation of the neutral kaon excitations with central masses less than1.5GeV/c2.The axial vector pair(K1(1270)-K1(1400))is interesting because it is a(coherent)mixtureof the singlet1P1and the triplet3P1states[3],parameterized by the mixing angleΘ:K1(1270)=−3P1·sinΘ+1P1·cosΘand K1(1400)=3P1·cosΘ+1P1·sinΘ.The ra-diative decay widths of the kaon excitations,Γr(K∗)=Γ(K∗→K+γ),are sensitive to the magnetic moments of the constituent quarks[4].Radiative widths have been calculated forlow-lying mesons using both a dynamic quark model[5]and a relativistic quark model[6,7]. Experimentally,onlyΓr(K∗(892))has been measured[8]so far.The Primakoffeffect[9],i.e.excitation by the Coulombfield,can be used to measure radiative widths since it is the inverse of radiative decay.In this Letter,we use the full dataset collected during the1996-97run of the KTeV experiment at Fermilab to study Primakoffproduction in two channels:the six-body K∗(892)π0channel,exemplified by K∗(1410)or K1(1400)→K∗(892)π0→[K Sπ0]π0→[(π+π−)(γγ)](γγ),which has twoπ0’s,and the four-body K Sπ0channel,exemplified by K∗(892)or K∗(1410)→K Sπ0→(π+π−)(γγ), which has a singleπ0.In the K∗(892)π0channel,we observe147candidate events which are predominantly the axial vector K1(1400)with a small admixture of K1(1270).Using a large sample of K∗(892)’s from the K Sπ0channel for normalization,we report thefirst measurements of the radiative widths for the axial vector pair.We also use the K Sπ0channel to place thefirst upper limit onΓr(K∗(1410))and a stringent upper limit onΓr(K∗2(1430)).For high particle energies and small production angles,the rate of exciting a K L to a K∗in the Coulombfield of a nucleus A is given by[10]dσ2S K+1 Γ(K∗→K+γ)t2|f EM|2,(1)whereαis thefine structure constant,Z is the atomic number of the nucleus,S K and S K∗are the spins of K L and the resonance,respectively,k=(m2K∗−m2K)/2m K∗,t is the magnitude of the square of the momentum transfer and t′=t−t min,√passed through a regenerator which was located∼124m from the target.The regenerator consisted of84modules of2cm-thick plastic scintillator followed by a module composed of a lead-scintillator sandwich.Since the Primakoffeffect is proportional to Z2of the target material,more than98%of the observed Primakoffexcitations(equation1)were produced in thefinal lead pieces.The regenerator was instrumented with photomultiplier tubes which enabled us to tag and reject backgrounds from inelastic interactions.We detectπ+π−tracks from K S decays using a drift chamber spectrometer system and photons fromπ0decays using a pure CsI electromagnetic calorimeter.The event trigger was initiated by signals from two scintillator hodoscopes located downstream of the spectrometer and required hits in the drift chambers consistent with two oppositely charged tracks.The decay volume was surrounded by a near-hermetic set of devices to veto photons.In the offline analysis,thefiducial region for the decay vertex of K S→π+π−is restricted to15m downstream of the regenerator.We reconstructπ0’s using pairs of energy clusters in the calorimeter.The clusters are required to have energies greater than1GeV and photon-like spatial distributions.To reject electrons,we require that the ratio of energy deposited in the calorimeter to the particle momentum as measured by the spectrometer be<0.8.To reconstruct the K∗(892)→K Sπ0decays used for normalization,in the four-body channel we require the invariant masses of theγγand theπ+π−to be within10MeV/c2of theπ0and K S invariant masses,respectively.We isolate Primakoff(forward)production by demanding that the square of the transverse momentum(p2t)of theπ+π−γγwith respect to a line connecting the target and the decay vertex of K∗(892)be less than0.001(GeV/c)2. We further requireπ+π−p2t>0.01(GeV/c)2because the daughter K S recoils against the π0.The resulting sample of29,399K∗(892)→K Sπ0decays with K S energy between30 and210GeV,and the K∗(892)energy between55and225GeV is shown infigure2(top).The requirements for the K∗(892)π0six-body channel are similar,except for changes to account for the extraπ0and differences in kinematics.The photon pairings for the twoπ0’sto the known masses are determined using aχ2formed by comparing Mγγand Mπ+π−γγofπ0and K∗(892),respectively.The K Sπ0mass for the daughter K∗(892)is required to be within101MeV/c2(two mass-widths)of the K∗(892)mass and its p2t to be>0.03(GeV/c)2. The p2t cut also serves to eliminate background from Primakoff-produced K∗(892)’s when accompanied by an accidentalπ0.To eliminate events in which two kaons decay to a charged and a neutral pion pair,we remove events for which the four-photon invariant mass is within 20MeV of the K L mass.The resulting sample of(K Sπ0)π0events with total energy greater than90GeV is depicted infigure3and shows a clustering near1.4GeV/c2.The mass projection shows the resonant signature exhibited by events with p2t<0.001(GeV/c)2and the p2t projection shows the sharp fall-offconfirming Primakoffproduction.There are147 events within the massfiducial region(1.1-1.64GeV/c2).Figure4shows the invariant mass and p2t of the daughter K∗(892)where the p2t displays a Jacobian distribution expected of a daughter particle in a two-body decay.The possible candidates for the observed K∗(892)π0resonance are K∗0(1430),K(1460), K∗(1410),K∗2(1430),K1(1270),and K1(1400)(figure1).The selectivity of the Primakoffef-fect rules out K∗0(1430)and K(1460)because of spin-parity conservation and the J=0→J=0 selection rule,respectively.Contributions from the vector K∗(1410)and tensor K∗2(1430)can be eliminated because both have significant branching fractions to K Sπ0[1],yet we see no ev-idence for their presence in this(K Sπ0)channel;note the lack of resonance near1.4GeV/c2infigure2(bottom).Wefit a combination of K∗(892)and K∗(1410)(K∗2(1430))simula-tions to the data and confirm that the signal from K∗(1410)(K∗2(1430))in the K Sπ0channel is consistent with zero:4.0±6.0(0.1±3.8)K∗(1410)(K∗2(1430))ing the known branching fractions[1]of K∗(1410)and K∗2(1430)to K Sπ0and K∗(892)π0,we translate these results into a negligible2.4±3.6(0.0±0.7)event contribution of K∗(1410)(K∗2(1430))in the K∗(892)π0channel.Thus we are left with only the axial vector pair(K1(1270)-K1(1400)) as a possible candidate for the observed resonance in the K∗(892)π0channel.We cross-checked the axial vector nature of the observerd signal using the distributions of Gottfried-Jackson(GJ)angles†θandφ.These distributions generally confirm our axial vector assignment.However,due to the relatively strong angular dependence of the detector acceptance,they do not have strong discrimination power between the axial vector pair and K∗(1410)and K∗2(1430).We now compute the radiative widths for the axial vector pair.It is difficult to decompose the mass spectrum of the observed signal into K1(1270)and K1(1400)because their mass separation is comparable to their widths.Nonetheless,mass information alone tells us that the contribution from K1(1270)is slight:only8.8±8.6events are due to K1(1270).However, a significantly better resolution is possible because the Primakoffeffect can produce only the singlet(1P1)component of the axial vector pair[13]and the singlet-triplet mixing angleΘhas been ingΘ=56±3◦[2]together with the known branching ratios of K1(1270) and K1(1400),we resolve the observed signal into11.4±1.0(stat)±4.1(ext syst)K1(1270) events and134.4±11.1(stat)∓4.1(ext syst)K1(1400)events,where the(external)system-atic error is due to the measurement uncertainties in the mixing parameterΘand in the K1(1270)and K1(1400)branching fractions to the K∗(892)π0channel.This decomposition, depicted infigure3,leads toΓr(K1(1270))=73.2±6.1(stat)±8.2(int syst)±27.0(ext syst) keV andΓr(K1(1400))=280.8±23.2(stat)±31.4(int syst)±25.4(ext syst)keV,where we have used our K∗(892)sample(figure2)for normalization purposes sinceΓr(K∗(892)) is known experimentally[8].Our measurements share internal systematic errors of8.7% due to uncertainties in the strong production(discussed below),6.6%due to detector accep-tance effects,and2.4%due to the3.6event uncertainty in the possible contributions from K∗(1410)and K∗2(1430),as discussed earlier.The uncertainty in the K∗(892)radiative width measurement[8]causes an additional8.5%(external)systematic error.Primakoffproduction is characterized by a sharp(∼t−1)forward production(equation1) allowing a strict p2t<0.001(GeV/c)2cut which virtually eliminates all potential back-grounds;seefigure3.Based on an extrapolation from the large p2t(>0.1(GeV/c)2)region, we estimate1.2events out of147signal candidate events to be due to incoherent production and other possible backgrounds such as those from the decay products of theΛ’s andφ’s produced when neutrons in the beam interact with the regenerator.Coherent strong production and its interference(with unknown strength)with Primakoffproduction are expected to be small at our energies[8].Indeed,a maximum likelihoodfit in the p2t variable for the strong production and the strength of the strong-Coulomb interference using the prescription given in[8,14]indicates that the strength of interference preferred byour data is consistent with zero.A constructive(destructive)interference would mean that the actual number of Primakoffevents is less(more)than what we observe.The mean change in our estimate of Primakoffproduction corresponding to one standard deviation variation in the interference strength is8.7%,which we have taken to be the systematic error due to the uncertainties in strong production.Earlier,we used the absence of a resonance in the K Sπ0channel at∼1.4GeV/c2(figure2) to limit the K∗(1410)and K∗2(1430)contributions to the observed(K1(1270)-K1(1400)) axial vector pair signal.A further benefit of thisfinding is that we are able to limit the radiative widthsΓr(K∗(1410))andΓr(K∗2(1430))to52.9and5.4keV,respectively,at90% CL.Γr(K∗(1410))has not been examined experimentally before,whereasΓr(K∗2(1430))was previously limited to84keV at90%CL[8].TheΓr(K∗2(1430))limit is far stricter than theΓr(K∗(1410))limit principally because the branching fraction for K∗2(1430)→K Sπ0is substantially larger[1]than the same for K∗(1410)→K Sπ0.The predicted radiative widths for the axial vector mesons[15],are538keV for K1(1400) and175keV for K1(1270);compare to our results,280.8±46.6keV and73.2±28.9keV, respectively.We note that the theoretical model in[15]is very sensitive to the quark masses (m u,s)and rms momenta(βuu,us,ss)of the quarks within the mesons.The predictions are based on certain choices for m andβ,but other choices with up to30%variation in m are possible.Our90%CL upper limit on the vector K∗(1410)radiative width is52.9keV.In the naive quark model,this state is thefirst radial excitation of K∗(892)and its radiative width calculation should be similar to that for K∗(892),for whichΓr(K∗(892))=116.5±9.9 keV[8].The smaller value for K∗(1410)may be due to a reduced overlap of the quark wavefunction for this higher radial excitation,but further guidance from theory is needed.Finally,we have substantially improved the upper limit on the radiative width of the tensor K∗2(1430)from84keV[8]to5.4keV(at90%CL).Babcock and Rosner[13]used SU(3)invariance to predict that excitations with J P C=1++or2++would have vanishing radiative widths.In the limit of SU(3),K∗2(1430)has C=+1;thus,our limit lends support to Babcock and Rosner’s prediction[13]and serves as a direct test of the naive quark model and SU(3)-breaking.We thank J.Bronzan for theoretical guidance and gratefully acknowledge the support and effort of the Fermilab staffand the technical staffs of the participating institutions for their vital contributions.This work was supported in part by the U.S.Department of Energy,The National Science Foundation and The Ministry of Education and Science of Japan.In addition,A.R.B.,E.B.and S.V.S.acknowledge support from the NYI program of the NSF;A.R.B.and E.B.from the Alfred P.Sloan Foundation;E.B.from the OJI program of the DOE;K.H.,T.N.and M.S.from the Japan Society for the Promotion of Science; and R.F.B.from the Funda¸c˜a o de Amparo`a Pesquisa do Estado de S˜a o Paulo.P.S.S. acknowledges receipt of a Grainger Fellowship.FIGURESP 1.5J 0.520.751.001.25K (1400)1 3 111 P + 1 P 0112+ + - 3 12 S K*(1410)10GeV/c - + 21 P K* (1430) 32 S K(1460)0 1 0 0 31 P K* (1430) 20 11 S K 0 131 S K*(892)1K (1270)FIG.1.Mass vs.angular momentum and parity (J P )for neutral kaon resonances.Arrows indicate resonances accessible by Primakoffexcitation.2FIG.2.Top:K S π0invariant mass in the four-body channel showing K ∗(892)→K S π0decays.Bottom:The same K S π0invariant mass in the 1.4GeV/c 2region.K ∗2(1430)and K ∗(1410)simulations are also shown to arbitrary scale.No K ∗2(1430)or K ∗(1410)resonance is apparent.(K0)π0 Invariant Mass (GeV/c 2)p t 2 ((G e V /c )2)(K S π0)π0 Invariant Mass (GeV/c 2)E v e n t s / 77 (M e V /c 2)02040608010012000.0050.01(K S π0)π0 P t 2(GeV/c)2FIG.3.Top:(K ∗(892)π0)p 2t vs.invariant mass after all other cuts.Bottom Left:Projection onto the abscissa after the p 2t cut.Decomposition of the observed signal into K 1(1270)and K 1(1400)is also shown.Bottom Right:Projection onto the ordinate after the mass cut.Note the sharply forward nature of Primakoffproduction.((GeV/c)2)Mass (GeV/c2)p2tFIG.4.Data/MC comparisons for the K Sπ0invariant mass(left)and the p2t for the 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